Question

A cone of radius 14 cm and height 35 cm is melted to form spherical balls each of radius 1.75 cm. Find the number of spherical balls formed.
1. 220
2. 172
3. 320
4. 285
5. 250

Answer 1

Correct Answer - Option 3 : 320

Concept Used:

When a cone is melted into sphere, then the volume of both is same.

Formula Used:

Volume of sphere = (4/3)πr³

Volume of cone = (1/3)πr²h

Calculations:

Let the number of spherical balls formed be n.

Radius of cone = 14 cm

Height of cone = 35 cm

Radius of spherical ball = 1.75 cm

(1/3)πr2h = n × (4/3)πr3

⇒ (1/3)π × (14)2 × 35 = n × (4/3)π(1.75)3

⇒ n = 320

∴ The number of spherical balls formed is 320.